Shaped-field hollow beam electron gun having high beam perveance and high beam convergence ratio



April 18, 1967 CHAOCHEN WANG 3,315,110

SHAPED`FIELD HOLLOW BEAM ELECTRON GUN HAVING HIGH BEAM FERVEANCE ANDHIGH BEAM CONVERGENGE RATIO Filed Aug. l2, 1965 4 Sheets-Sheet l CHA@CHE/V WANG ATTORNEY April 18, 1967 CHAO CHEN WANG 3,315,110

SHAPED-FIELD HOLLOW BEAM ELECTRON GUN HAVINC. HIGH BEAM PERVEANCE ANDHIGH BEAM CONVERGENCE RATIO Filed Aug. 12, 1965 4 Sheets-Sheet 2 ma wiApril 18, 1957 CHAO CHEN WANG 3,315,110

SHAPED-FIELD HOLLOW BEAM ELECTRON GUN HAVING HIGH l BEAM PERVEANCE ANDHIGH BEAM CONVRGINCE RATO 1963 4 Sheets-Sheet 3 Filed Aug. l2

B BACK EDGE ELECTRON B FRONT EDGE ELECTRON INVENTOR. CHAO CHE/v WANG BY@JW ,en

A TUR/VH April 18, 1967 CHAO CHEN WANG 3,315,110 SHAPED-FIELD HOLL OWBEAM ELECTRON GUN HAVING HIGH BEAM PERVEANCE AND HIGH BEAM CONVERGENCERATIO 1965 4 Sheets-Sheet 4 Filed Aug. l2,

NORMAL To EMITTmG SURFACE PARALLEL l FLU L INE CENTRIFUGAL FORCE LORENTZFORCE BACKWARD COMPONENT CENTER AXIS I NON PARALLEL NORMAL To \\r FLUXUNE /J'EMlsSu/E SURFACE v EMISSIVE RESULTANT FORCE CENFTRUGAL SURFACE oE FLUX INVENTQR. JUNE CHAO CHE/V WANG -`-CENTER A TTO/WVEY `high powerlevels and/or high frequencies.

United States Patent Sperry Rand Great Neck, N.Y., a corporation of Thisinvention relates to producing a hollow electron high convergence ratio,and a low noise figure.

Most of the klystron and traveling wave tubes presently in operationemploy a solid pencil electron beam that is coupled to electromagneticwaves supported on a suitable standing wave or traveling wave structure.It has been found that the solid electron beams have serious limitationswhen employed in tubes intended to operate at These limitations resultfrom the fact that the space charge forces in the solid beam limit thecurrent obtainable in a well focused beam, for a given operatingvoltage, thus limiting the power output obtainable with such a solidbeam. Additionally, the electromagnetic waves interact only with thoseelectrons in the outer regions of the beam so that the electrons in thecent-er portion of the beam are largely wasted and only contribute tothe production of the harmful space charge effects. For these reasons,considerable attention has been directed to producing hollow electronbeams which possess the advantages of requiring lower operating voltagesfor a given power output and high beam perveance, and hence widerbandwidth and improved eliiciencies of operation.

Because of the electrical current limitations of presently availablecathodes, electron beams having high current density must have highconvergence ratios, wherein convergence ratio is understood to mean theratio of the cathode emitting surface area to the focused electron lbeamarea. In general, it may be said that with given limitations on thecurrent emission of the cathode and on the physical size of theinteraction circuits, the limit on the power output of an electron beamtube is proportional to the ratio an electron beam gun for beam havinghigh perveance,

(convergence ratio) /3 (perveance 2/3 lHigh perveance beams are desiredfor high power tubes, but unless the convergence ratio can be increasedaccord- 'igly, no actual increase in power output is achieved.

One type of hollow beam gun that has been the subject of considerableinterest is the so-called magnetroninjection gun that is disclosed inU.S. Patent 2,632,130, issued March 17, 1953 to J. F. Hull, and which isthe subject of investigation in an article entitled The Design andPerformance of a Magnetron-Injection Gun, by Kino and Taylor, appearingon pages l-ll of the January 1962 issue of IRE Transactions on ElectronDevices. The authors Kino and Taylor describe a hollow beam guncomprised of an emitting cathode having the shape of a truncated rightcircular cone wherein the right circular cone has a half-angle ofapproximately 4. Associated with this cathode is an anode whichproducesan electrostatic iield having an axial component which tends todraw out in an axial direction the electrons which are orbiting aboutthe cathode due to the presence of an axially-directed magnetic focusinglield. While the magnetron-injection gun of the type disclosed in theabovecited reference has found use in lower power tubes in the lowermicrowave frequency ranges, attempts to adapt them for use in high powertubes and in the high freagain places a limitation on is limited to thevalue 3,315-,1 l0 Patented Apr. 18, 1967 quency ranges have been lesssuccessful because the convergence ratios obtainable are limited, thebeams are noisy, and the electron emission is intolerably non-uniformover the emissive surface of the cathode.

The limitations on the convergence ratio of the knownmagnetron-injection gun arises from the fact that the cathode used inthese guns is in the form` of a truncated right circular cone, and withsuch a cathode the convergence ratio must 'be lower than the value sinwhere qs is the half-angle of the truncated cone. This aboverelationship indicates that the half-angle of the cathode must fbe smallin order to achieve higher convergence ratios. Limiting the half-angleof the conical cathode places a limitation on the magnitude of the axialcomponent of the electric eld at the emitting surface, and this has theeffect of permitting the orbiting electrons to remain for a longer timein the cathode region, thus increasing the possibilities `for theelectron collisions and interactions that contribute to the noise on thebeam. Patentee Hull has observed that the diameter of the base of theytruncated conical cathode must not exceed the diameter of the apertureof the anode, the reason being that should this occur the electronswould strike the anode and the noise on the beam would increase. Thisthe convergence ratio that may be obtained with the magnetron-injectiongun.

I have discovered that I can avoid the above-mentioned limitations byemploying a concept lbased upon the use of a specially shaped magneticfocusing field, this shaped -lield being characterized -by havingmagnetic flux lines that are substantially straight, parallel, and.closely grouped in the central region of the field, but which divergeradially in a flare in the end region of the fie-ld and again becomemore closely grouped at their outer radii. The cathode is placed in thisend region with -the electron emissive surface conforming to, orslightly inclined backwardly with respect to the flaring 4magnetic fluxlines. With this arrangement, the convergence ratio no `longer sin qband the emitting surface may have a considerable radial extent along theflaring ux line, thereby increasing the emissive surface area, and thusthe convergence ratio and also producing a larger axial component in theanodecathode electric field that tends to ldraw the orbiting electronsout of the cathode region, thereby to minimize the noise on the ibeamand promote uniform emission from the electron emissive surface.

The high convergence ratio comes about fromthe fact that electrons tendto follow the magnetic` lines of force from the cathode to the highvoltage beam. region. With this greatly divergent magnetic ield shape,the magnetic field helps to compress the beam that originated at theemissive surface having large radii throughout its `length to a muchsmaller radius at the: high voltage focused beam region.

It therefore is an object of this invention. to provide an electron beamgun that produces a hollow electron beam having a high convergence ratioand a high perveance.

Another object of this invention is to provide an electron beam gun thatproduces a hollow beam having high perveance and high convergence ratio,and is characterized by substantially uniform emission from the cathodesurface.

A further object of this invention is to provide a relatively stable andnoise free hollow electron beam having high convergence ratio and highperveance.

A further object of this invention is to provide a hollow electron beamgun of the magnetron-injection type having a relatively large electronemissive surface.

Another object of this invention is to provide an electron beam gun thatutilizes a shaped magnetic field to compress the electrons emitted froma cathode surface of large radius to a focused hollow beam of muchsmaller radius.

Still another object of this invention is to produce a hollow electronbeam by means of a cathode having an electron emissive surface that isimmersed in and proportioned in shape with respect to a shaped magneticfocusing field.

The present invention will be described by referring to the accompanyingdrawings wherein:

FIG. l is a perspective view, partially broken away, showing thecathode, anode, and focusing electrodes of the hollow beam gun of thepresent invention;

FIG. 2 is a somewhat schematic sectional view of electron gun of FIG. 1showing the positions and shapes of the various components relative tothe contour of the fiux lines of the magnetic focusing field;

FIG. 3 is a sectional view similar to FIG. 2 and further showing, in arepresentative way, the formation of the hollow electron beam from theemitting surface of a cathode of this invention;

FIGS. 4, 5 and 6 are graphs used in explaining the design and operationof the hollow electron beam gun of this invention;

FIG. 7 is a simplified sectional illustration of an alternativeembodiment of a hollow electron beam gun constructed in accordance withthe teachings of the present invention;

FIG. 8 is a graph used in explaining the design and operation of theelectron beam gun illustrated in FIG. 7.

FIGS. 9 and 10 are illustrations of alternative embodiments of thepresent invention; and,

FIGS, ll and 12 are diagrams used in explaining the forces due to themagnetic field that act on electrons with different magnetic fieldpatterns.

Referring now in detail to the drawing, a hollow electron beam gunconstructed in accordance with the teachings of this invention isillustrated in FIGS. l and 2 and is comprised of focusing coil 11 andbucking coil 12 having like poles adjacent each other to produce amagnetic field having the pattern illustrated by the dashed lines 14that represent the magnetic fiux lines. As illustrated, fiux lines 14extend parallel and axially throughout the interaction region of thetube and diverge outwardly in a nonlinear flare in the end region of thefield. As used in this description, nonlinear is intended to mean that astraight line relationship does not exist throughout -the flared region.Coils 11 and 12 are normally disposed exteriorly of the tube envelopewhile of course the cathode, anode, focusing electrodes and the like arewithin the tube envelope.

Other arrangements may be employed for producing a magnetic fieldpattern of the desired shape. For example, one or more permanent magnetsmay be used, or combinations of permanent magnets and solenoids may beused. All these arrangements may include magnet pole pieces, if desired.

Cathode 17, which is in the form of a figure of revo'- lution, ispositioned in the end region of the magnetic focusing field where theflux lines 14 diverge outwardly. The electron emissive surface 18 of thecathode 17 is disposed along the nonlinearly contoured sides of thecathode, and this surface is shaped to conform to the curvature of amagnetic fiux line, or fiux tube, upon which it lies. An annular anodeelectrode 2t) is disposed coaxially in spaced-apart relationship aboutthe electron emissive surface 18 and extends axially beyond the smallerend of cathode 17, thus providing an electric field having a largeaxially-directed component to draw the spiraling electrons in an axialdirection from emissive surface 18. As may be seen, the electric fieldbetween the anode 20 and the back portion of cathode 17 that is of thelargest diameter will be substantially wholly axially, thus drawing outthe electrons from this back portion so as to decrease the possibilityof electron interaction in this region, thus reducing the noise on thebeam and promoting good electron emission from the rear of the surface18.

Electrostatic focusing electrodes 23 and 24 are positioned respectivelyat the front and rear edges of electron emissive surface 18 to aid infocusing the hollow electron beam. A drift tube 25 together with thedesired interaction circuit (not illustrated) extend to the right of theIt will be seen that the outwardly diverging surface 18 of cathode 17provides considerably more electron emissive surface area than isavailable on the truncated right circular cone shaped cathode of theknown prior art. For comparison purposes, for a given increase in uthelength at the back end of a cathode, the emissive surface of the shapedfield hollow beam gun of this invention will increase by a largerpercentage than will the cathode of the known prior art having the shapeof a truncated right circular cone. This results from the fact that therear area of the cathode of this invention will increase more nearly asthe increasing area of a circle, while the increasing area of the priorart surface 'will be in accordance with the equation for the curvedsurface of the truncated right circular cone.

The formation of the thin hollow beam from the emissive surfaceillustrated in FIGS. 1 and 2 is represented by the sketch of FIG. 3wherein it is seen that electrons emitted from the front edge ofemissive surface 18 find an equilibrium position at the inner edge ofthe focused beam and electrons emitted fromthe back edge of the emissivesurface find an equilibrium position at the outer edge of the focusedbeam. Electrons emitted from the intermediate areas of the emissivesurface 18 find equilibrium positions between the inner and outer edgesof the focused beam. Thus, the compression of the electrons from thecathode surface of large radii into a smaller diameter hollow beam isclearly evident from FIG. 3, and results from the specially shapedmagnetic field which has the converging flux lines that are more closelygrouped at the front end of the gun.

In order to arrive at the design objectives for an electron gunconstructed in accordance with the present invention, and in order todetermine its limitations, the following theoretical background ispresented. However, before getting into the details of the theory to befollowed, it will be helpful to keep in mind that the general approach,is to provide a shaped magnetic focusing field wherein the fielddiverges outwardly in a nonlinear flare, and then position in thediverging region of the field an electron emitting surface having adefinite relationship to the contour of the magnetic flux lines -of theshaped field. For this reason it is necessary that an initial step inthe design procedure be that the shape and magnitude of the magneticfocusing field be determined as accurately as possible.

It is assumed that the magnetic focusing field is axially symmetricalabout a longitudinal axis which constitutes the central axis of theelectron beam tube in which the gun is to be used. Therefore, the fluxlines that are illustrated -by the dashed lines in the drawings -arerepresentative of axially symmetrical lines of fiux of tubelike form. Itis further assumed that the electrons in the hollow beam travel with acommon axial velocity. Since the electrons in the beam repel each other,there is always present a spreading force due to space charge within thebeam. In order to maintain the hollow shape of the beam, other forcesmust be employed to neutralize the effects of this space charge force.These other forces are the Lorentz force due to the electrons cuttingthe magnetic field lines, the centrifugal force due to the lis theLorentz force.

orbiting motion of the forces due to electric focusing electrodes.

Referring to FIG. 3, consider an electron located at the axial positionZ2 at a radius r from the axis of the axially symmetrical magneticfield, whose magnitude B is a function of r and Z. This same electronoriginated on the cathode emissive surface at an axial position Z1. Ataxial position Z2, the circle of radius ra encloses the same magneticflux as was originally enclosed by the same electron at position Z1 onthe cathode surface. For a substantially uniform magnetic field, theproduct B13,2 represents the initial magnetic vector potential of theelectron. It is known from Buschs theorem of conservation of magneticmomentum that the angular frequency of an electron is electrons, and theelectric field potentials of the anode and the is the Larmor frequency,ratio of an electron. tion is defined as the e/m being the charge tomass The positive sense of angular rotamechanical angular momentum inthe same direction as the magnetic vector potential. A negative 6 willresult in a radial lLorentz force which decelerates the electron movingaway from the axis or accelerates it toward the axis. A consequence ofusing Buschs theorem is that the angular velocity of an electron in anaxial symmetric magnetic field, once the conditions at the cathode areestablished and known, is a function of its position only. A moreimportant consequence, so far as the design of the shaped-field hollowbeam gun of this invention is concerned, is that it deals only with therelationships between the flux at the cathode and that in the focusedhollow beam, without having to consider what happens to the electrons inbetween these places. This means that there is considerable flexibilityin positioning the cathode, once the shape of the magnetic field isknown.

- Asa consequence of Buschs theorem we may express the forces that areavailable in the focused hollow beam to neutralize the space chargeforce by the following expression, which dimensionally is in units ofelectric field,

wherein ILe/m. The first term on the right side of Equation 2 is thecentrifugal force and the second term In this development, Lorentz forceis dened as being equal to [--e(v B)], where e and B are as previouslydened and v is the velocity of the electron. This definition omits theelectric field term E which sometimes is included. The sign of F ispositive when the force is directed outwardly from the axis.

Because the space charge ES varies in the radial direction, i.e., rEs isa variable, the product of radius and the constant electric eld rEL,provided by external electrodes cannot neutralize the space chargeforce. It is for this reason that the most important objective ofmagnetic focusing of a high density hollow beam is to derive a maximumvariation of rF among electrons within the narrowest belt of radialspace.

To examine this force rF, Equation 1 may be substituted into Equation 2to give the following:

'in FIGS. 4 and 5.

FIGS. 4 and 5 will It will be further helpful to rewrite Equation 3 inthe form which is plotted in FIG. 6. This graph shows the forces at agiven radius r as a function of the angular velocity relative to theLarmor frequency and also shows the maximum negative force availablewhen the angular velocity equals the Larmor frequency, i.e.,

To compare the focusing of the hollow beam with that of the well-knownBrillouin focusing technique for a solid beam, reference may be made toan article by applicant entitled, Electron Beams in Axially SymmetricalElectric and Magnetic Fields, appearing on pages 147 of the February1950 issue of Proceedings of the I.R.E. In this article Applicantteaches that the minimum magnetic lield strength required for Brillouinfocusing of a solid beam is at the point A in FIG. I6, and the magnitudeof this field, is given by the expression raf Bmnfrzoar 7) wherein K isthe microperveance of the beam, V is the beam operating voltage, and ris the beam radius. If an ,electron is emitted from a cathode whichencloses magnetic flux, the operating range on the curve of FIG. 6 willshift to the right of point A, that is,to the ABOC portion of thecurve,if the ux through the cathode is in the same direction as the mainmagnetic focusing field. The operating range will shift to the left ofpoint A, the AEL portion `of the curve, if the direction -of themagnetic flux enclosed by the cathode opposes the direction of the mainmagnetic focusing field. This latterI portion of the curve AEL is oflittle interest, however, because of the diiculty of producing a beamthat -will work well in the transition region from one direction ofmagnetic lield to the other. Also, because there is mirror symmetry ofthe curve about the point A, forces corresponding to points on theportion of the curve ABOC involve less angular velocity than points onthe portion of the curve AEL that represent the same amount of force.vTherefore, by using the portion of the curve ABOC, more axiallydirectedkinetic energy is available in the beam for interaction withelectromagnetic waves.

The portion of the curve ABOC of FIG. 6 is indicated by similar letterdesignations on the curve of FIG. 5. In FIGS. 4 and 5, the conditions ofzero angular velocity and zero force correspond to the points r=ra. Asmay lbe seen of FIG. 4, the Larmor frequency -wL that is designated bythe point A in FIG. 6 is reached only when the operational radius r islarge in comparison with ra. The limit corresponding to point A in FIG.6 is indicated in FIG. 5 by the dashed curve -wL2r2/i7. For the focusingof the hollow electron beam in accordance with this invention, whereinra has a linite value, references to show that the operational range Bof FIG. 6 has an angular rotational frequency less than the Larmorfrequency, and the negative force available for focusing the beam isless than the maximum obtainable force for a given magnetic fieldstrength. When r is less than ra the curves of FIGS. and 6 show that theforce F becomes positive. As seen in FIG. 4, when r is very much smallerthan ra, 6 is very large, the Equation 2 indicates that when thiscondition exists the centrifugal force is predominant. Otherwise, thecentrifugal force is relatively small compared to the Lorentz force.

For most practical uses of a hollow electron beam, such as in travelingwave tubes and klystron tubes, the beam will be surrounded by a metalliccircuit and all the electric field lines emanating from the space chargewill terminate on this metallic conductor. With this condition present,there will be no electric force on the inside edge of the beam so thatthe balancing force there also must be zero. For this reason, theoperational points on FIGS. 4 and 5 for the electrons on the inner edgeof the hollow beam are on the zero 9 and rF axes where r=ra. Theoperational point for electrons on the outer edge of the hollow is inthe region of FIG. 5 designated B, at a radius r=r0 and the electronsbetween the edges fall on the portion of the solid curve designated OB.

It can be shown that to have a complete equilibrium beam with forcesbalanced at all points within the beam, the space charge densitydistribution should follow the wherein p0,L is space charge density atthe inner edge of the beam. The electrostatic field Es that results fromthe space charge density distribution expressed in Equation 8 has thefollowing form:

where w'ea-:npoa/eo is the square of the plasma frequency at radius ra,e0 being the permittivity of a vacuum.

Comparing Equations 4 and 9, it will be seen that the space charge forceis balanced by the sum of the Lorentz force and the centrifugal forcewhen 4 (l0) To compare the magnetic field required to focus a hollowbeam with that required to focus a solid beam having the same 6, the`plasma frequency we and the Larmor frequency for the solid beam caseare related by the expression The subscript m indicates the minimummagnetic field case. In order to keep the same total perveance and thesame outer radius for the two cases, we must have From the above, theratio of the Larmor frequency to the minimum Larmor frequency required,is

at 2 1 (may mi CLm 2 wem 704- Ta.4

the same space charge forces and the focusing force F on the outerelectrons of both beams will be the same because was assumed to be thesame in -both cases. Equation 14 therefore indicates that with anarrangement as illustrated in FIG. 2 wherein the electron emissivesurface is shaped and positioned to conform to an outwardly aringmagnetic fiux line, a hollow electron beam having an inner radius of raand an outer radius of ro may be produced with a magnetic focusing fieldhaving a magnitude of B gauss.

Again, the advantages arising from the use of the cathode constructed inaccordance with this invention are that the cathode emitting area may bemade much larger for a given linear length than with the truncated rightcircular cone cathode. Further, because of the outward flares of theemitting surface and the anode, the electric field normal to theemissive surface has a very large component in the axial direction, thusdrawing the electrons from the cathode surface and thereby reducingnoise and producing more uniform emission from the emitting surface. Thenet accomplishment is the creation of a higher perveance beam havinglower noise, and without `the necessity for any sacrifice in theconvergence ratio or increase in the strength of the magnetic focusingfield.

For the purpose of the above investigation it was assumed that electronsfrom the front and back edges of emissive surface 18 reached equilibriumpositions, respectively, at the inner and outer edges of the focusedbeam. It should be understood that it is a theoretically assumedcondition which may be achieved in practice, although this does notinvalidate the above development.

An alternative embodiment of the present invention is illustrated insimplified form in FIG. 7 and enables one to obtain an even thinnerhollow beam with a given focusing magnetic field strength than with thearrangement illustrated in FIGS. 1 and 2. In the embodiment of FIG. 7,the back end of the cathode is tilted back- Wardly from the magneticfiux line on which the front edge of the cathode is coincident so thatthe electrons emitted from the back edge of the cathode are at a lowermagnetic vector potential than those emitted from the front edge. Thefocusing forces on the electrons emitted from the front and back edgesof the emitting surface 38 of FIG. 7 are illustrated in the diagram ofFIG. 8 in which the curve 40 illustrates the magnitude of the forcesacting on electrons emitted with the same magnetic vector potentialBit,2 as an electron emitted from the `front edge of emitting surface38. Curve 41 represents the magnitude of the forces acting on electronsemitted with the same magnetic vector potential Br02 as an electronemitted from the back edge of emitting surface 38. The solid line 44represents the forces acting on the electrons emitted from the regionbetween the front and back edges of the emitting surface 38 of FIG. 7.It may be seen that the thickness (rol-ra) of the focused beam is lessin this embodiment than it would be (ro-ra), in the embodiment of FIGS.1 and 2. In a practical situation this means that for a given beamthickness the magnetic field may be less than indicated by Equation 13,or for the same magnetic field strength, the convergence ratio can bemade larger. Conversely, it is true that a thicker beam will result, andhence a lower convergence ratio, if the electron emissive surface istilted the other way so that the back edge of the surface is at a highermagnetic vector potential than the front edge. This has been experiencedin the use of the prior art magnetroninjection gun that employs asubstantially uniform axial magnetic field.

It Will be noticed that by tilting the emissive surface toward the rearthe cathode-anode electrostatic field at the emissive surface has lessof an axially directed component. However, by assuring that the magneticfield flux lines extend outwardly as radially as possible, the cathodemay be tilted backwardly with respect to a flux line and yet permit thecathodeaanode electrostatic field to have an appreciable axialcomponent.

Maximum advantage may be taken of the axial electric field between theanode and cathode by an embodiment of the invention illustrated insimplified form in FIG. 9, wherein the electron emissive surface 68 ofthe cathode 70 is positioned and shaped to conform to the extremeoutwardly extending port-ion of the flaring tubelike lines of flux.Front and back focusing electrodes 71 and 72 serve the same function asthat previously described for the corresponding electrodes in theelectron gun illustrated in FIGS. l and 2. In this embodiment of theinvention, the projection of the emissive surface 68 onto a plane normalto the center axis of the tube is very large while the projection of thesurface 68 onto a plane parallel to the center axis is quite smallwhereby the electric field gradient between anode 74 and emissivesunfaice 68 is very nearly axial so that electrons are emitted fromsurface 68 with a very large initial axial velocity, thereby promotinguniform emission and low noise. Furthermore, the outer radius at theback end of emissive surface 68 is quite large so that the lconvergenceratio achieved with this embodiment of the invention will beconsiderably larger than with the previously described embodiments. Theprinciples of operation of the electron gun of FIG. 9 is the same alsfor the previously described embodiments of the invention.

Another shaped-eld hollow beam electron gun constructed in accordancewith the teachings of this invention is illustrated in FIG. 10 whereinthe focusing magnetic field is shaped to present parallel flux lines inthe central region of the field, but in the end region of the eld the uxlines liare outwardly and reverse their slopes at the far radial extentof the field. In this instance, electron emissive surface 80 is shapedand positioned to conrform to the portions of flux lines 82 and 83having reverse slopes so that electrons emitted from surface `80 willinitially be directed inwardly toward the axis of the gun. Anodeelectrode 85 is positioned coaxially about ythe axis of the gun yin theforward region thereof so as to establish the proper electric field todraw the orbiting electrons into the focused beam. Focusing electrode`87 is positioned coaxially about the front edge of emissive surface 80and focus-ing electrode 88 is positioned about the central axis of thegun to aid in focusing the hollow beam. In this embodiment of theinvention the electrons emitted from the back edge of electron emissivesurface 80 theoretically will find equilibrium positions at lthe inneredge of the focusing hollow beam while the electrons emitted from thefront edge of electron emissive surface 80 will find their equilibriumpositions at the outer edge of the hollow beam. As may be seen from -thevarious embodiments of this invention previously described, there isconsiderable flexibility in designing an electron hollow beam gun inaccordance 'with the teachings of this invention. In all of theseembodiments large emissive surfalce.l areas, and hence large convergenceratios, are readily obtained for high perveance beams.

One further and important consideration must be given to the forcesacting on the electrons leaving the emissive surface of an electron gunconstructed in accordance with this invention, and this considerationfurther emphasizes the importance of producing the specially shapedmagnetic eld. This consideration involves the direction of the axialforce on the electrons due to the magnetic field. Obviously it isdesirable for optimum eiciency of operation that the axial forces due tothe electric and magnetic fields act in the same direction so as todirect the electrons toward the front end -of the gun. This condition,however, does not necessarily follow for all geometrical relationshipsbetween the shape and location of the electron emissive surface and themagnetic field flux lines. FIG. ll is a diagram used to illustrate thesituation in which the axial force on an electron e is in the backwarddirection, opposite the direction of the `force due to the electricfield established between the anode and cathode. In this discussion,forward and backward are in reference to a line normal to the electronemis- Y 10 sive surface 91. For simplicity, only one half of the cathodeis illustrated in FIG. l1, it being understood that the `cathode is afigure olf revolution that is symmetrical about the center axis, asillustrated in FIG. 1.

In FIG. ll the electron emissive surface 91 is shaped to conform to theoutwardly Haring flux line 93, and the iiux line 94 which is radiallyvbeyond emissive surface 91 is Iparallel to the flux line 93 in theregion of the emissive surface 91. The centrifugal fonce acting onelectron e is directed radially outwardly, and the Lorentz force actingon electron e is normal to flux line 94 and falls on top of the normalto the emitting surface 91 because the ux lines 93 and 94 are assumed to:be parallel. It may be seen that the resultant of the centrifugal forceand the Lorentz force falls in back of the normal to the emittingsurface and therefore has a hack-ward component force that would tend todirect electron e toward the rear of electron emissive surface 91.

Satisfactory operation of an electron ygun with the arrangementillustrated in FIG. l1, wherein the emissive surface is parallel -to theflux line 94 still is possible, the only result being that this type ofgun is not as efficient as possible because the cathode to anodeelectric field now must be large enough to overcome the backwardcomponent of the resultant magnetic lforce and to draw the electrons outof the front end of the gun. All of the theoretical considerations thatwent .into derivations of Equation 13 still are valid since they areconcerned only with the radial forces acting on electron e.

FIG. l2 illustratesthe situation wherein the axial force on an electrone due to the summation of the centrifugal force and the Lorentz forceproduces a for-wardly directed force component to urge the electron outof the front end of the gun, thus aiding the force due to thecathode-anode electric field. In the arrangement illustrated in FIG. l2,electron emissive surface 91 again is conformal` to Vthe flux line 93,but the ux `line which electron e is cutting is not parallel to the fiuxline 93 but is tilted backwardly so as to have less slope with respectto the axis in the central region of the emissive surface 91. Thecentrifugal force still is directed radially outward and the Lorentzforce, which is normal to flux line 95, now is in front of the linenormal to emissive surface 91. The resultant of the centrifugal forceand the Lorentz force also is on the forward side of the normal toemissive surface 91 and has a forwardly directed component of forcewhich urges the electron e out of the front end of the gun, thus aidingthe force due to the cathode-anode electric field. This relationshipbetween the slopes of the liux lines is more desirable than thatillustrated in FIG. 11 because the smaller anode voltage is required todraw the electrons from the gun.

Therefore, in summary, to produce a magnetic field in accordance withthe teachings of this invention, it is necessary to keep in mind thatthe radially more distant ux line 95 should have less slope than theflux line coincident with the emissive surface in the region of theemissive surface, or at least in the central region thereof, in orderthat the Lorentz force vector be in front of the normal line to theemissive surface. Further, to assure good compression, or convergenceratio the flux lines should be more closely grouped in the region at thefront of the gun and at the radially most distant regions of the field.

The magnetic field pattern having flux lines with the relationshipillustrated in FIG. 12 is relatively easy to obtain with conventionalsolenoids, magnets, and pole pieces that are commonly used in theconstruction of electron tubes.

In the design of a hollow beam gun in accordance with the presentinvention, the first step is to produce the magnetic focusing field thathas the shape just described and illustrated in the accompanyingdrawings. One way of producing such a field is by means of oppostelypolarized solenoids or permanent magnets placed end to end, with orwithout a pole piece therebetween. By using solenoids, the flare of themagnetic focusing field can be controlled over a large range. The shapeof the magnetic field is plotted either by using iron filings or amagnetic field probe.

The outer radius of the beam must conform to the size of the interactionstructure with which it is to be used, and since the inner radius of thebeam generally will be along the same fiux line as the front edge of theemissive surface, the desired flux line that the emissive surface is tofollow may be chosen in order to insure a given beam thickness.

Next the shape and position of the anode 20, FIG. 2, is determined inorder to provide an appreciable axial electric field, and to avoidintercepting the electrons since this reduces the beam current andincreases the noise on the beam. As a preliminary guide in arriving atthe anode shape, the so-called Hull cut-off lines may be used as astarting design. These lines are determined by the following equation lRoz z 45.48 RQ is the desired anode voltage, B is the measured magneticfield in gauss, Rc and RL are the radii of the cathode and anode,respectively, in centimeters. By employing known methods, the finaldesign and shape of the anode surface is determined.

After the shapes and positions of the electron emissive surface and theanode have been determined, the shapes, positions, and potentials of thefront and back focusing electrodes 23 and 24 of FIG. 2 are determined.These electrodes provide means for exercising a final control overelectron trajectories to further enable the designer to achieve thedesired beam characteristics. The shapes and positions of focusingelectrodes 23 and 24 may be arrived at with the aid of an electrolytictank and an analog computer, the procedure followed being known to thoseskilled in the art.

An electron gun constructed in accordance with the teaching of thisinvention had the following physical and electrical characteristics:

where V where relative beam thickness is defined as (beam outerradius)(beam inner radius) beam outer radius While the invention hasbeen described in its preferred embodiments, it is to be understood thatthe words which have been used are words of description rather thanlimitation and that changes within the purview of the appended claimsmay be made without departing from the true scope and spirit of theinvention in its broader aspects.

What is claimed is:

j 1. Electron gun means for producing a focused hollow electron beamdirected along a longitudinal axis, said gun comprising,

means for producing a magnetic field having lines of flux that extendradially outwardly from said axis at the back region of said gun andconverge with a nonlinear taper toward said axis at the forward regionof said gun, an electron emitting means positioned in the radially-outwardly extending portion of said magnetic field l2 and having anelectron emissive surface arranged in shape and positioned so that saidsurface generally follows the contour of those fiux lines lyingimmediately adjacent said surface and between the ends thereof, and

means for exerting an axially directed force on electrons emitted fromsaid emitting means to draw said electrons toward the front end of saidgun.

2. The combination claimed in claim 1 wherein said electron emittingmeans is a surface of revolution that extends at least in part in anaxial direction along said gun.

3. The combination claimed in claim 2 wherein said electron emittingsurface is substantially conformal to nonlinear lines of flux.

4. An electron beam gun adapted to produce an axially directed hollowelectron beam, said gun comprising,

electron emitting means having an axially extending electron emissivesurface in the shape of a figure 0f revolution having a first diameterat the front end thereof nearest the front of said gun and extendingoutwardly in a nonlinear liare to a second larger diameter at its rear,

means for producing a focusing magnetic field having fiux lines thatdiverge outwardly in a nonlinear fiare in the direction toward the rearof said gun,

said electron emitting means being immersed in said magnetic field in azone thereof wherein the lines of flux diverge outwardly in a nonlinearflare from the front end toward the rear of said electron emissivesurface,

means for exerting an axially directed force on electrons emitted fromsaid surface to draw said elec trons from said surface toward said oneend.

5. An electron beam gun adapted to produce an axially directed hollowelectron beam, said gun comprising,

electron emitting means having an axially extending electron emissivesurface in the shape of a figure: of revolution having a first diameterat the front. end thereof nearest the front of said gun and extend ingradially outwardly in a nonlinear flare to a sec-ond large diameter atits rear,

means for producing a focusing magnetic field having. flux lines thatdiverge outwardly in a nonlinear fiarey in the direction toward the rearof said gun,

Said electron emitting means being immersed in said magnetic field in aZone thereof wherein the lines of flux diverge outwardly in a nonlinearfiare from the front end toward the rear of said electron emissivesurface,

an anode electrode disposed in coaxial and spaced apart relationship tosaid emissive surface, the surface of said anode fiaring outwardly inthe direction toward the rear of said gun thereby to produce an axiallydirected component of electric field between said emissive surface andsaid anode.

6. Apparatus for producing a hollow electron beam directed along alongitudinal axis, said apparatus comprising,

means for producing an electron beam magnetic focusing field having fluxlines that extend radially outwardly at a first region and converge witha nonlinear taper toward said axis at a second region,

an electron emitting surface disposed about said axis in the region ofsaid magnetic field and having a shape substantially conforming to andcoincident with the lines of flux of said magnetic field, and

means for exerting an axially directed force on electrons emitted fromsaid surface to draw said electrons from said surface toward said secondregion.

7. Apparatus for producing a hollow electron beam directed along alongitudinal axis, said apparatus comprising,

means for producing a magnetic field that is symmetrical about said axisand has a pattern of flux lines that extend radially outwardly at afirst region and converge with a non-linear taper toward said axis at asecond region, an electron emitting surface disposed symmetrically aboutsaid axis in the region of said magnetic eld,

said surface extending radially outwardly in said first region of thefield and converging with a non-linear taper toward said axis at thesecond region of said field,

said emitting surface being non-conformal to the magnetic field fluxpattern with its end at said first region at a lower magnetic vectorpotential than its end adjacent said second region.

8. The combination claimed in claim 7 and further including,

an anode electrode disposed symmetrically about said axis in spacedapart relationship from said emissive surface,

said anode extending axially ybeyond said surface in said second regionof the magnetic field and diverging youtwardly with a nonlinear tiaretoward said first region.

9. An electron gun for producing a hollow elect-ron beam directed alonga longitudinal axis, said apparatus comprising,

means for providing an electron beam magnetic focusing field that ischaracterized by having a pattern of flux lines that are substantiallyaxially directed in a first region of said eld and are radiallydiverging with a nonlinear flare at a second region of said field,

electron emitting means comprising an electron emitting surfacesymmetrically disposed about said axis in said second region of thefocusing field where the flux lines diverge radially and having itssurface diverging in the direction in which said field diverges,

said electron emitting means being located so that the lines of fluxlying between the ends thereof and adjacent the said surface thereof andwhich are coincident with the surface of said emitting means at thefront end thereof will have a divergence not less than the divergence ofsaid surface.

10. Electron gun means for producing a focused hollow electron beamdirected along a longitudinal axis, said gun comprising,

means for providing an electron beam magnetic focusing field having apattern of iiux lines that converge toward said axis at a iirst regionand diverge radially in a nonlinear flare at a second region, the flareof said flux lines in said second region being characterized by havingslopes of one sense along their respective portions nearest said axisand having slopes of an opposite sense along their respective portionsmost distant from said axis, an electron emitting surface disposed aboutsaid axis in the second region of said magnetic field where the fluxlines have slopes of said opposite sense,

said surface facing inwardly to emit electrons toward said axis, and

means for exerting a force on said electrons to direct them toward saidfirst region. 11. An electron gun for producing a hollow electron beamdirected along a longitudinal axis, said apparatus comprising,

means for providing an electron beam magnetic focusing iield that ischaracterized by having a pattern of flux lines that are substantiallyparallel and axially directed in the central region of said eld andradially diverging with a nonlinear flare at an end region of saidfield, an electron emitting surface symmetrically disposed about saidaxis in said end region of the focusing field where the liux linesdiverge radially,

said emitting surface being conformal to the contour of the magneticfield flux pattern present at its location.

12. The combination claimed in claim 11 and further including,

an anode electrode disposed coaxially in spaced apart relationship aboutsaid emissive surface and extending beyond the end of said emissivesurface in the direction toward the central regionA of said field anddiverging radially in a nonlinear flare at its opposite end, thereby toproduce an axial component of electric field `between said anode andsaid emissive surface.

13. The combination claimed in claim including,

first and second focusing electrodes respectively positioned adjacentthe two ends of said emissive surface,

said electrodes being positioned and electrically biased to furthercontrol the shape of said hollow electron beam.

14. Apparatus for producing a hollow electron beam directed along alongitudinal axis, said apparatus comprising,

means for producing an electron ybeam magnetic focusing field havingflux lines that extend radially outwardly at a lirst region along saidaxis and converge with a nonlinear taper toward said axis at a secondregion axially displaced from said rst region,

an electron emitting surface disposed about said axis in the region ofsaid magnetic field and having a shape substantially conforming to andcoincident with the said iiux lines of said magnetic field.

15. The combination claimed in claim 14 wherein the flux line to whichsaid electron emitting surface conforms 50 has a greater slope in theregion of said surface than the flux lines that are radially moredistant from said surface.

12 and further References Cited by the Examiner UNITED STATES PATENTS2,306,875 12/1942 Fremlin S15-5.35 2,812,467 11/1957 Kompfner S15- 3.5

JAMES W. LAWRENCE, Primary Examiner. V. LAFRANCHI, Assistant Examiner.

11. AN ELECTRON GUN FOR PRODUCING A HOLLOW ELECTRON BEAM DIRECTED ALONG A LONGITUDINAL AXIS, SAID APPARATUS COMPRISING, MEANS FOR PROVIDING AN ELECTRON BEAM MAGNETIC FOCUSING FIELD THAT IS CHARACTERIZED BY HAVING A PATTERN OF FLUX LINES THAT ARE SUBSTANTIALLY PARALLEL AND AXIALLY DIRECTED IN THE CENTRAL REGION OF SAID FIELD AND RADIALLY DIVERGING WITH A NONLINEAR FLARE AT AN END REGION OF SAID FIELD, AN ELECTRON EMITTING SURFACE SYMMETRICALLY DISPOSED ABOUT SAID AXIS IN SAID END REGION OF THE FOCUSING FIELD WHERE THE FLUX LINES DIVERGE RADIALLY, 